For those who are new to these trilogy comic book series, I recommend reading the the Promise trilogy before reading the Search.

Avatar: The Last Airbender - The Promise

The Promise takes place after the war where Fire Lord Zuko and Avatar Aang have to deal with aftermath of the war, moving Fire Nation colonies that are in the Earth Kingdom.

This series of digests rejoins Aang and friends for exciting new adventures, beginning with a faceoff against the Fire Nation that threatens to throw the world into another war, testing all of Aang's powers and ingenuity!

Story by Gene Luen Yang and Art by Gurihiru.

The Search is about Fire Lord Zuko searching for his mother. Fans will finally find out what happened to her.

Avatar: The Last Airbender - The Search

Crunchyroll has some preview shots. I arranged in order. Since it's not a manga, it's read from left to right just to inform you. I had the same confusion when I read the Promise Part 1 for the first time.

After the season 1 of Legend of Korra has grossed in an average of 3.8 million viewers, Nickelodeon has officially contracted 26 more episodes. They assumed that these episodes will be split into two books. The original contract for the television series has not ended yet since Nickelodeon signed for 26 episodes which 14 already aired in Season 1, Book 1 (April 14, 2012 - June 23, 2012). The remaining episodes will premiere in 2013 as Season 1, Book 2 to finish the original contract.

The Legend of Korra (2012)

For those who are new to Legend of Korra, here is a synopsis written by Wales.

Synopsis

Seventy years after the Hundred Years War, Avatar Aang has passed on and the time has come for the new Avatar to be selected. Finding a young waterbender named Korra, it is evident she is the new Avatar as she sets off to begin her training of the four elements. Already having mastered fire, earth, and water at a remarkably early age, she has one element left to master: air. With a mass shortage of airbenders in the world, the responsibility is left to a man who knew Aang too well: his youngest son Tenzin. However, Tenzin cannnot train Korra in the South Pole so she must relocate to Republic City; the iconic city Aang and Fire Lord Zuko created to be a center of peace in the world between benders and non-benders.

However, Korra quickly discovers that beneath the beauty of the city lies the underbelly of crime as well as a growing anti-bending revolution that threatens to tear republic city apart. Knowing that her responsibilities involve keeping the city peaceful, she discovers new allies in the form of pro-bending brothers Mako and Bolin and an even greater threat than she ever could have imagined. The leader of The Equalists, Amon. Behind the mask is a scarred man who has a power that makes even the quick tempered and fierce Avatar crumble to her knees.